Constructing a Cut Ellipse Surface via Rotation and Partitioning

This example demonstrates how to build an “elliptical surface” by starting from an ellipse-related curve, rotating it to form a 3D surface, and then cutting/partitioning that surface to reveal structured, fractal-like patterns. The key mathematics includes ellipse/curve modeling in Cartesian (or parametric-like) form, surface generation by revolving a curve, geometric cutting to obtain intersection regions, and the role of function/transform parameters in producing different structural outcomes (closely aligned with the iterative intuition behind fractal geometry). Construction is driven by GeoGebra commands and objects: Surface to create the surface; CurveCartesian to define the generating curve in Cartesian coordinates (e.g., objects like f and d); and Rotate to revolve/transform parts of the configuration into a 3D surface (objects such as r, R, w, v, c). Finally, additional constructed objects (including pairs like b and b' plus other intermediate elements) are used to perform the cut/partitioning of the surface, producing visible subdivided bands and sectional shapes. Suitable for high school to early university geometry lessons, especially for students learning coordinate geometry, 3D surface modeling, and dynamic/interactive geometry construction.